單擺式滑動隔震系統於水平垂直雙向地震力作用下之曲面效應理論與實驗探討

Curvature effect on seismic responses of pendulum sliding isolators subjected to vertical and horizontal bi-directional ground excitations

10.6849/SE.201706_32(2).0003

蔡諄昶(Chun-Chung Tsai)；盧煉元(Lyan-Ywan Lu)；王亮偉(Liang-Wei Wang)；鍾立來(Lap-Loi Chung)

滑動隔震 ； 摩擦單擺支承 ； 曲面效應 ； 耦合效應 ； 垂直震波 ； 極限地震力 ； 雙向地震力 ； base isolation ； sliding isolation ； pendulum isolator ； curvature effect ； bi-direction excitation ； centrifugal force

結構工程

32卷2期（2017 / 06 / 01）

65 - 90

繁體中文

摩擦單擺支承(FPS)為目前使用最廣之滑動式隔震支承，該類支承之滑動面為具有固定曲率半徑之圓球面，以便提供隔震系統所需之回復力，並以滑動摩擦提供系統所需之消能能力。目前常用之FPS隔震分析模型多以一固定勁度之彈簧及定摩擦之元件加以並聯而成。此種模型係假設支承位移遠小於曲率半徑故支承回復勁度近似常數，同時忽略滑動曲面傾角對回復力及摩擦子正向力之影響。此種簡化式模型在支承位移較小時或可提供足夠的精度，但在極大地震力或具速度脈衝特性之近斷層震波作用下，支承位移與速度有可能急速增加，此時滑動曲面效應對隔震動力行為即可能產生可觀之影響。為能補捉FPS隔震系統於極大地震力作用下之真實隔震行為，本文以拉格朗運動方程式推導該系統於水平與垂直雙向震波同時作用下之完整運動方程式。經由本文所推導之方程式可知，FPS隔震系統之水平與垂直向運動方程式實應包含二個與曲面斜率及曲率相關之非線性高階項，同時此二項又分別與支承水平滑動加速度及速度相關，因而造成隔震系統垂直與水平運動間之耦合效應，並產生額外之垂直向加速度及支承軸壓力等效應，本文經由振動台實驗並進一步證實此耦合效應之存在。本文進一步利用所推導之完整分析模型，並採用168筆不同強度之水平與垂直雙向震波以進行剛性結構之隔震模擬。初步研究結果顯示，支承曲面效應對於隔震結構水平向反應(水平上傳加速度與支承位移)之影響較為有限，但對於隔震結構之垂直向反應(垂直上傳加速度與支承正向力)則有較大之影響。若忽略曲面效應可能低估垂直向反應達20%以上，部份震波甚至可達40%以上。

Friction pendulum system (FPS) isolator is one of most widely used sliding isolators, presently. This type of isolators usually has a spherical sliding surface with constant radius, in order to produce a restoring force for the isolation system. The energy dissipation of the isolator is provided by sliding friction force. The common model adopted for an FPS isolator usually contains a constant-stiffness spring and a friction element placed in parallel. This model assumes that the isolator displacement is much smaller than the radius of the sliding surface, therefore the curvature and slope effects of the spherical surface on the restoring and friction forces can be neglected. This simplified model may not be applicable for FPS isolators under earthquakes that produce large isolator displacements or sliding velocities, since in these earthquakes the curvature and slope of the sliding surface may have significant effects on the dynamic response of the isolation system. In order to capture the actual response of a FPS-isolated structural system under an extreme earthquake, in this paper, complete dynamic equations of motion for the isolation system under vertical-and-horizontal bi-directional ground excitations were derived by using Lagrange's equation. It is shown that the derived governing equations in both horizontal and vertical directions contain high-order nonlinear terms related to the slope and curvature of the sliding surface. These terms that are functions of horizontal sliding velocity and acceleration cause the coupling effect between horizontal and vertical motions and result in extra vertical acceleration and isolator axial load. The existence of the coupling effect was further verified by the shaking table test conducted in this study. In addition, by using the derived complete dynamic equations, the time responses of a FPS-isolated rigid structure under 168 ground motions with different intensities and characteristics were simulated. The simulation result demonstrates that the high-order terms have less effect on the horizontal response (acceleration and isolator drift) of the isolated system, but are more influential on the vertical responses (acceleration and isolator axial load). Neglecting the high-order terms may underestimate the vertical response by about 20-40% in a sever earthquake.

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